PLC-based LP11 mode rotator for mode-division multiplexing transmission Kunimasa Saitoh,1,* Takui Uematsu,1 Nobutomo Hanzawa,2 Yuhei Ishizaka,1 Kohei Masumoto,1 Taiji Sakamoto,2 Takashi Matsui,2 Kyozo Tsujikawa,2 and Fumihiko Yamamoto2 2
1 Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan NTT Access Network Service Systems Laboratories, NTT Corporation, 1-7-1 Hanabatake, Ibaraki 305-0805, Japan * [email protected]
Abstract: A PLC-based LP11 mode rotator is proposed. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide. Numerical simulations show that converting LP11a (LP11b) mode to LP11b (LP11a) mode can be achieved with high conversion efficiency (more than 90%) and little polarization dependence over a wide wavelength range from 1450 nm to 1650 nm. In addition, we fabricate the proposed LP11 mode rotator using silica-based PLC. It is confirmed that the fabricated mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. ©2014 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.4510) Optical communications.
References and links 1.
E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, Y. Luo, G. D. Peng, G. Li, and T. Wang, “6 × 6 MIMO transmission over 50+25+10 km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper OTu2C.4. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6192056 2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). 3. M. Salsi, C. Koebele, D. Sperti, P. Tran, H. Mardoyan, P. Brindel, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. B. Astruc, L. Provost, and G. Charlet, “Mode-division multiplexing of 2 × 100 Gb/s channels using an LCOSbased spatial modulator,” J. Lightwave Technol. 30(4), 618–623 (2012). 4. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Mode-division multiplexed transmission with fiber mode couplers,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW1D.4. 5. A. Li, J. Ye, X. Chen, and W. Shieh, “Low-loss fused mode coupler for few-mode transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3G.4. 6. S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, and J. Bland-Hawthorn, “Mode-selective photonic lanterns for space-division multiplexing,” Opt. Express 22(1), 1036–1044 (2014). 7. S. Yerolatsitis, I. Gris-Sánchez, and T. A. Birks, “Adiabatically-tapered fiber mode multiplexers,” Opt. Express 22(1), 608–617 (2014). 8. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, M. Koshiba, and F. Yamamoto, “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express 21(22), 25752–25760 (2013). 9. T. Uematsu, K. Saitoh, N. Hanzawa, T. Sakamoto, T. Matsui, K. Tsujikawa, and M. Koshiba, “Low-loss and broadband PLC-type mode (de)multiplexer for mode-division multiplexing transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh1B.5. 10. N. Hanzawa, K. Saitoh, T. Sakamoto, K. Tsujikawa, T. Uematsu, M. Koshiba, and F. Yamamoto, “Three-mode PLC-type multi/demultiplexer for mode-division multiplexing transmission,” in European Conference and Exhibition on Optical Communication 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper Tu.1.B.3. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6647527 11. T. Uematsu, N. Hanzawa, K. Saitoh, Y. Ishizaka, K. Masumoto, T. Sakamoto, T. Matsui, K. Tsujikawa, and F. Yamamoto, “PLC-type LP11 mode rotator with single-trench waveguide for mode-division multiplexing
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19117
transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.52. 12. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19(3), 405–413 (2001).
1. Introduction An expansion of the transmission capacity per fiber is needed because of the rapid growth of Internet traffic in the optical fiber network. Mode-division multiplexing (MDM) has attracted attention to obtain a much larger transmission capacity. The mode (de)multiplexer is an important component to realize MDM transmission. Various mode (de)multiplexers based on free-space optics [1–3], fiber coupler and a long-period fiber bragg grating (LPFBG) [4,5], photonic lantern [6], adiabatically-tapered fiber [7], and planar lightwave circuit (PLC) [8,9] have been demonstrated. PLC-based mode (de)multiplexer has unique advantages including a low insertion loss, relatively low wavelength dependence, a small size, and high mass productivity due to the adoption of mature semiconductor manufacturing technologies such as photolithography and ion etching. The PLC-based mode (de)multiplexer is one of the promising mode (de)multiplexers for the purpose of mass production. We have proposed the PLC-based threemode multiplexer which can multiplex and excite LP01, LP11a, and LP21 modes [10]. The PLC-based mode multiplexer which can excite LP11b mode is required to realize a mode (de)multiplexer which can multiplex LP01, LP11a, LP11b, and LP21 modes. However, the PLCtype mode multiplexer which can excite LP11b mode has not been presented because it is difficult to excite electronic waveguide modes Emn (n ≥ 2) like LP11b mode in the same plane. In this paper, we design and fabricate a PLC-based LP11 mode rotator for the excitation of LP11b mode [11]. Numerical simulations show that converting LP11a mode to LP11b mode can be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also show that the LP11 mode rotator can convert LP11b mode to LP11a mode, has little polarization dependence, and has a good fabrication tolerance. We finally fabricate the proposed LP11 mode rotator using silica-based PLC and confirm that the fabricated LP11 mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. 2. Principle and design Figure 1 shows the structure of the PLC-based LP11 mode rotator. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide as shown in Fig. 1. The degree of the asymmetry can be controlled by changing the trench position t, the trench width s, and the trench depth d. By properly designing the trench parameters, two orthogonal LP11 modes whose optical axes are rotated by around 45° with respect to the x- and y-axes propagate in the waveguide with the trench as shown in Figs. 2(a) and 2(b), and the two orthogonal LP11 modes are equally excited and propagated with different propagation constants, β1 and β2, in the waveguide with the trench when LP11a (LP11b) mode is launched. By setting the length of the waveguide with the trench to a half beat-length, π/(β1 – β2), LP11a (LP11b) mode is rotated into LP11b (LP11a) mode.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19118
Fig. 1. Structure of a PLC-based LP11 mode rotator with a trench. Inset images show field distributions of LP11a and LP11b modes.
Fig. 2. Field distributions of two orthogonal LP11 modes whose optical axes are rotated with respect to the x- and y-axes in the waveguide with the trench; (a) 1st LP11 mode, (b) 2nd LP11 mode.
In this paper, we assume that the proposed mode rotator is based on silica-based PLC with a relative refractive index difference Δ between the core and cladding of 0.45% [10], and the waveguide width w and height h are respectively set to w = 11.3 μm and h = 11.0 μm in order to reduce the coupling loss between PLC waveguide and a two-mode fiber to be connected. One can choose other values for Δ, w, and h as you desire. Next, we choose design parameters related to the trench such as the trench position t, width s, and depth d. When t, d, and s are chosen to large values, the device length tends to be short because the difference of the propagation constants, β1 and β2, between two orthogonal LP11 modes becomes larger. However, crosstalk to undesired modes such as LP01 mode and undesired back reflections become higher when t, d, and s are chosen to large values due to the mode field mismatch at the boundary between the waveguides with and without the trench. Thus, t, d, and s should be chosen to small values in order to suppress the crosstalk to undesired modes. In this paper, we chose target parameters of t = 2.0 μm and s = 1.5 μm for easy fabrication. Figure 3(a) shows d dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes shown in Fig. 2 at a wavelength of 1550 nm, where t = 2.0 μm and s = 1.5 μm. From Fig. 3(a), d should be chosen to d = 5.4 μm for the overlap of LP11a mode with the two orthogonal LP11 modes shown in Fig. 2 to be equivalent. Figure 3(b) shows t dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes at a wavelength of 1550 nm with d = 5.4 μm and s = 1.5 μm, and Fig. 3(c) shows s dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes at a wavelength of 1550 nm with d = 5.4 μm and t = 2.0 μm. It can be seen that the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes can be controlled by changing t, d, and s. Finally, the length of the mode rotator L is set to L = 1.46 mm, which equals the half beat-length of the two orthogonal LP11 modes shown in Fig. 2. The designed parameters are
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19119
shown in Table 1. It has been numerically confirmed that the undesired back reflection at the boundary between the waveguides with and without the trench is lower than −30 dB when the designed parameters in Table 1 are used.
(a)
(b)
(c) Fig. 3. (a) Trench depth d, (b) trench position t, and (c) trench width s dependence of normalized overlap integral of 1st and 2nd LP11 modes shown in Fig. 2 with LP11a mode at a wavelength of 1550 nm.
Figure 4 shows the calculated conversion efficiency as a function of the length of the proposed mode rotator for x- and y- polarization when (a) LP11a mode or (b) LP11b mode is input at a wavelength of 1550 nm. The inset images show the field distributions of LP11 mode #212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19120
in the mode rotator at each propagation length. Red and blue solid lines show the result for xpolarization. Green and cyan dashed lines show the result for y-polarization. We used the fullvector finite-element beam propagation method [12] for numerical simulations. From Fig. 4, we can see that LP11a (LP11b) mode is converted into LP11b (LP11a) when L equals 1.46 mm, and there is little polarization dependence because two lines for x- and y- polarization almost overlap each other. The polarization dependence in the PLC-based mode rotator with small index difference between core and cladding is negligibly small, however, it may become large if the core-cladding index difference increases. Table 1. Design Parameters of the Proposed LP11 Mode Rotator. Δ 0.45%
w 11.3 μm
h 11.0 μm
L 1460 μm
t 2.0 μm
d 5.4 μm
s 1.5 μm
(a)
(b) Fig. 4. Conversion efficiency as a function of the trench waveguide length for x- and ypolarization when (a) LP11a mode or (b) LP11b mode is input at a wavelength of 1550 nm. Inset images show field distributions of LP11 mode in the LP11 mode rotator. Red and blue solid lines show the results for x-polarization. Green and cyan dashed lines show the results for ypolarization. Two lines almost overlap each other owing to little polarization dependence. See Media 1.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19121
(a)
(b) Fig. 5. Wavelength dependence of the LP11 mode rotator when (a) LP11a mode or (b) LP11b mode is input.
3. Characteristics Figure 5 shows the calculated wavelength dependence of the LP11 mode rotator when (a) LP11a mode or (b) LP11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 5, the wavelength dependence of the conversion efficiency is negligible (more than 90% over a wavelength range from 1.45 μm to 1.65 μm), and the crosstalk to the input LP11 mode is less than −20 dB over a wavelength range from 1.5 μm to 1.6 μm for both polarizations. Figure 6 shows the fabrication tolerance of the LP11 mode rotator when LP11a mode is launched at a wavelength of 1550 nm. The conversion efficiency is insensitive to fabrication errors and the crosstalk to the input LP11 mode is less than −20 dB when t, d, and s change by ± 0.3 μm, ± 0.4 μm, and ± 0.1 μm, respectively. The actual fluctuation through PLC fabrication will depend on a fabrication process and it is usually in the order of submicron.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19122
(a)
(b)
(c) Fig. 6. Fabrication tolerance to (a) trench position t, (b) trench depth d, (c) trench width s when LP11a mode is input at a wavelength of 1550 nm.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19123
(a)
(b)
(c) Fig. 7. Wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of the design parameters shown in Table 1 (t = 2.0 μm, d = 5.4 μm, and L = 1.46 mm) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19124
(a)
(b)
(c) Fig. 8. Wavelength dependence of the normalized output power for the case of t = 1.0 μm, d = 4.3 μm, and L = 1.92 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19125
(a)
(b)
(c) Fig. 9. Wavelength dependence of the normalized output power for the case of t = 0 μm, d = 3.9 μm, and L = 2.99 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19126
Next, we consider reducing the crosstalk to undesired modes such as LP01 mode and the input LP11 mode. Figure 7 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 7(a), LP01 mode is output (without polarization conversion) when LP01 mode is input. This is because the optical axis for the LP01 mode is not rotated by the small trench. As shown in Fig. 7, the crosstalk to the undesired modes is less than −16 dB over a wavelength range from 1.45 μm to 1.65 μm. The crosstalk can be improved by making the parameters related to the trench smaller values. Figure 8 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of t = 1.0 μm, d = 4.3 μm, and L = 1.92 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched. From Figs. 7 and 8, we can see that the crosstalk to the undesired modes is reduced from −16 dB to −18 dB when the trench parameters are set to be smaller values. Figure 9 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of t = 0 μm, d = 3.9 μm, and L = 2.99 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched. The crosstalk to the undesired modes is reduced from −16 dB to −23 dB when the trench parameters are set to be smaller values as shown in Figs. 7 and 9.
Fig. 10. Fabricated LP11 mode rotator with silica-based PLC. All components are fabricated on a chip. Upper and lower waveguides do not have and have the trench, respectively.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19127
Fig. 11. Experimental setup for the LP11 mode rotator. PLC-based mode multiplexers are used for excitation of LP11a mode.
4. Fabrication Figure 10 shows the fabricated LP11 mode rotator using silica-based PLC with the target structural parameters shown in Table 1. All components shown in Fig. 10 are fabricated on a chip. Figure 11 shows the experimental setup for the LP11 mode rotator. In the experiment, we observed near field patterns of output light through a waveguide with or without the trench when LP11a mode is input. LP11a mode should be output when LP11a mode is input to the waveguide without the trench. On the other hand, rotated LP11 mode (ideally LP11b mode) should be output when LP11a mode is input to the waveguide with the trench. We used the PLC-based two-mode multiplexer [8] to excite LP11a mode. Table 2 shows the near field patterns of output light through the waveguide with (the left column of Table 2) or without (the right column of Table 2) the trench when LP11a mode is input at each wavelength. The reason of rotation of LP11 mode with the change of wavelength is because the optimum half beat-length for 90 degree rotation is depending on the wavelength. From Table 2, we can confirm that the fabricated LP11 mode rotator converts LP11a mode to LP11b mode over a wide wavelength range from 1460 nm to 1600 nm. We can obtain PLC-based three-mode (de)multiplexer for LP01, LP11a, and LP11b modes when we utilize the proposed LP11 mode rotator and the two-mode (de)multiplexer [8]. Figure 12 illustrates the schematic drawing of the PLC-based three-mode multiplexer that can multiplex and demultiplex LP01, LP11a, and LP11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers [8] and the proposed LP11 mode rotator. Two-mode multiplexers are used for excitation of LP11a mode. All components can be fabricated on a chip. LP11b, LP01, and LP11a modes are output when LP01 modes are launched to port 1, port 2, and port3, respectively.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19128
Table 2. Near Field Patterns of Output Light Through the Fabricated Waveguide with (Left) or without (Right) a Trench when LP11a Mode is Input at Each Wavelength Index profile
With a trench
Without a trench
Wavelength
1460 nm
1480 nm
1500 nm
1520 nm
1540 nm
1550 nm
1560 nm
1580 nm
1600 nm
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19129
Fig. 12. Schematic drawing of PLC-based three-mode multiplexer that can multiplex and demultiplex LP01, LP11a, LP11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers and the proposed LP11 mode rotator. Two-mode multiplexers are used for excitation of LP11a mode.
5. Conclusion We have designed and fabricated the PLC-based LP11 mode rotator for the excitation of LP11b mode. Numerical simulations showed that converting LP11a mode to LP11b mode could be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also showed that the LP11 mode rotator could convert LP11b mode to LP11a mode, had little polarization dependence, and had a good fabrication tolerance. It was clarified that the crosstalk to the undesired modes could be suppressed by making the trench smaller. We finally fabricated the proposed LP11 mode rotator using silica-based PLC and confirmed that the fabricated LP11 mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. We can realize the PLCbased three-mode (de)multiplexer for LP01, LP11a, and LP11b modes when we utilize the proposed LP11 mode rotator and the two-mode (de)multiplexer [8].
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19130
1 Graduate School of Information Science and Technology, Hokkaido University, Sapporo 060-0814, Japan NTT Access Network Service Systems Laboratories, NTT Corporation, 1-7-1 Hanabatake, Ibaraki 305-0805, Japan * [email protected]
Abstract: A PLC-based LP11 mode rotator is proposed. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide. Numerical simulations show that converting LP11a (LP11b) mode to LP11b (LP11a) mode can be achieved with high conversion efficiency (more than 90%) and little polarization dependence over a wide wavelength range from 1450 nm to 1650 nm. In addition, we fabricate the proposed LP11 mode rotator using silica-based PLC. It is confirmed that the fabricated mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. ©2014 Optical Society of America OCIS codes: (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.4510) Optical communications.
References and links 1.
E. Ip, N. Bai, Y.-K. Huang, E. Mateo, F. Yaman, M.-J. Li, S. Bickham, S. Ten, J. Liñares, C. Montero, V. Moreno, X. Prieto, Y. Luo, G. D. Peng, G. Li, and T. Wang, “6 × 6 MIMO transmission over 50+25+10 km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper OTu2C.4. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6192056 2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 × 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). 3. M. Salsi, C. Koebele, D. Sperti, P. Tran, H. Mardoyan, P. Brindel, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. B. Astruc, L. Provost, and G. Charlet, “Mode-division multiplexing of 2 × 100 Gb/s channels using an LCOSbased spatial modulator,” J. Lightwave Technol. 30(4), 618–623 (2012). 4. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Mode-division multiplexed transmission with fiber mode couplers,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper OW1D.4. 5. A. Li, J. Ye, X. Chen, and W. Shieh, “Low-loss fused mode coupler for few-mode transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTu3G.4. 6. S. G. Leon-Saval, N. K. Fontaine, J. R. Salazar-Gil, B. Ercan, R. Ryf, and J. Bland-Hawthorn, “Mode-selective photonic lanterns for space-division multiplexing,” Opt. Express 22(1), 1036–1044 (2014). 7. S. Yerolatsitis, I. Gris-Sánchez, and T. A. Birks, “Adiabatically-tapered fiber mode multiplexers,” Opt. Express 22(1), 608–617 (2014). 8. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, M. Koshiba, and F. Yamamoto, “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express 21(22), 25752–25760 (2013). 9. T. Uematsu, K. Saitoh, N. Hanzawa, T. Sakamoto, T. Matsui, K. Tsujikawa, and M. Koshiba, “Low-loss and broadband PLC-type mode (de)multiplexer for mode-division multiplexing transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh1B.5. 10. N. Hanzawa, K. Saitoh, T. Sakamoto, K. Tsujikawa, T. Uematsu, M. Koshiba, and F. Yamamoto, “Three-mode PLC-type multi/demultiplexer for mode-division multiplexing transmission,” in European Conference and Exhibition on Optical Communication 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper Tu.1.B.3. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6647527 11. T. Uematsu, N. Hanzawa, K. Saitoh, Y. Ishizaka, K. Masumoto, T. Sakamoto, T. Matsui, K. Tsujikawa, and F. Yamamoto, “PLC-type LP11 mode rotator with single-trench waveguide for mode-division multiplexing
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19117
transmission,” in Optical Fiber Communication Conference/National Fiber Engineers Conference 2014, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.52. 12. K. Saitoh and M. Koshiba, “Full-vectorial finite element beam propagation method with perfectly matched layers for anisotropic optical waveguides,” J. Lightwave Technol. 19(3), 405–413 (2001).
1. Introduction An expansion of the transmission capacity per fiber is needed because of the rapid growth of Internet traffic in the optical fiber network. Mode-division multiplexing (MDM) has attracted attention to obtain a much larger transmission capacity. The mode (de)multiplexer is an important component to realize MDM transmission. Various mode (de)multiplexers based on free-space optics [1–3], fiber coupler and a long-period fiber bragg grating (LPFBG) [4,5], photonic lantern [6], adiabatically-tapered fiber [7], and planar lightwave circuit (PLC) [8,9] have been demonstrated. PLC-based mode (de)multiplexer has unique advantages including a low insertion loss, relatively low wavelength dependence, a small size, and high mass productivity due to the adoption of mature semiconductor manufacturing technologies such as photolithography and ion etching. The PLC-based mode (de)multiplexer is one of the promising mode (de)multiplexers for the purpose of mass production. We have proposed the PLC-based threemode multiplexer which can multiplex and excite LP01, LP11a, and LP21 modes [10]. The PLC-based mode multiplexer which can excite LP11b mode is required to realize a mode (de)multiplexer which can multiplex LP01, LP11a, LP11b, and LP21 modes. However, the PLCtype mode multiplexer which can excite LP11b mode has not been presented because it is difficult to excite electronic waveguide modes Emn (n ≥ 2) like LP11b mode in the same plane. In this paper, we design and fabricate a PLC-based LP11 mode rotator for the excitation of LP11b mode [11]. Numerical simulations show that converting LP11a mode to LP11b mode can be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also show that the LP11 mode rotator can convert LP11b mode to LP11a mode, has little polarization dependence, and has a good fabrication tolerance. We finally fabricate the proposed LP11 mode rotator using silica-based PLC and confirm that the fabricated LP11 mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. 2. Principle and design Figure 1 shows the structure of the PLC-based LP11 mode rotator. The proposed mode rotator is composed of a waveguide with a trench that provides asymmetry of the waveguide as shown in Fig. 1. The degree of the asymmetry can be controlled by changing the trench position t, the trench width s, and the trench depth d. By properly designing the trench parameters, two orthogonal LP11 modes whose optical axes are rotated by around 45° with respect to the x- and y-axes propagate in the waveguide with the trench as shown in Figs. 2(a) and 2(b), and the two orthogonal LP11 modes are equally excited and propagated with different propagation constants, β1 and β2, in the waveguide with the trench when LP11a (LP11b) mode is launched. By setting the length of the waveguide with the trench to a half beat-length, π/(β1 – β2), LP11a (LP11b) mode is rotated into LP11b (LP11a) mode.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19118
Fig. 1. Structure of a PLC-based LP11 mode rotator with a trench. Inset images show field distributions of LP11a and LP11b modes.
Fig. 2. Field distributions of two orthogonal LP11 modes whose optical axes are rotated with respect to the x- and y-axes in the waveguide with the trench; (a) 1st LP11 mode, (b) 2nd LP11 mode.
In this paper, we assume that the proposed mode rotator is based on silica-based PLC with a relative refractive index difference Δ between the core and cladding of 0.45% [10], and the waveguide width w and height h are respectively set to w = 11.3 μm and h = 11.0 μm in order to reduce the coupling loss between PLC waveguide and a two-mode fiber to be connected. One can choose other values for Δ, w, and h as you desire. Next, we choose design parameters related to the trench such as the trench position t, width s, and depth d. When t, d, and s are chosen to large values, the device length tends to be short because the difference of the propagation constants, β1 and β2, between two orthogonal LP11 modes becomes larger. However, crosstalk to undesired modes such as LP01 mode and undesired back reflections become higher when t, d, and s are chosen to large values due to the mode field mismatch at the boundary between the waveguides with and without the trench. Thus, t, d, and s should be chosen to small values in order to suppress the crosstalk to undesired modes. In this paper, we chose target parameters of t = 2.0 μm and s = 1.5 μm for easy fabrication. Figure 3(a) shows d dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes shown in Fig. 2 at a wavelength of 1550 nm, where t = 2.0 μm and s = 1.5 μm. From Fig. 3(a), d should be chosen to d = 5.4 μm for the overlap of LP11a mode with the two orthogonal LP11 modes shown in Fig. 2 to be equivalent. Figure 3(b) shows t dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes at a wavelength of 1550 nm with d = 5.4 μm and s = 1.5 μm, and Fig. 3(c) shows s dependence of the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes at a wavelength of 1550 nm with d = 5.4 μm and t = 2.0 μm. It can be seen that the normalized overlap integral of LP11a mode with 1st and 2nd LP11 modes can be controlled by changing t, d, and s. Finally, the length of the mode rotator L is set to L = 1.46 mm, which equals the half beat-length of the two orthogonal LP11 modes shown in Fig. 2. The designed parameters are
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19119
shown in Table 1. It has been numerically confirmed that the undesired back reflection at the boundary between the waveguides with and without the trench is lower than −30 dB when the designed parameters in Table 1 are used.
(a)
(b)
(c) Fig. 3. (a) Trench depth d, (b) trench position t, and (c) trench width s dependence of normalized overlap integral of 1st and 2nd LP11 modes shown in Fig. 2 with LP11a mode at a wavelength of 1550 nm.
Figure 4 shows the calculated conversion efficiency as a function of the length of the proposed mode rotator for x- and y- polarization when (a) LP11a mode or (b) LP11b mode is input at a wavelength of 1550 nm. The inset images show the field distributions of LP11 mode #212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19120
in the mode rotator at each propagation length. Red and blue solid lines show the result for xpolarization. Green and cyan dashed lines show the result for y-polarization. We used the fullvector finite-element beam propagation method [12] for numerical simulations. From Fig. 4, we can see that LP11a (LP11b) mode is converted into LP11b (LP11a) when L equals 1.46 mm, and there is little polarization dependence because two lines for x- and y- polarization almost overlap each other. The polarization dependence in the PLC-based mode rotator with small index difference between core and cladding is negligibly small, however, it may become large if the core-cladding index difference increases. Table 1. Design Parameters of the Proposed LP11 Mode Rotator. Δ 0.45%
w 11.3 μm
h 11.0 μm
L 1460 μm
t 2.0 μm
d 5.4 μm
s 1.5 μm
(a)
(b) Fig. 4. Conversion efficiency as a function of the trench waveguide length for x- and ypolarization when (a) LP11a mode or (b) LP11b mode is input at a wavelength of 1550 nm. Inset images show field distributions of LP11 mode in the LP11 mode rotator. Red and blue solid lines show the results for x-polarization. Green and cyan dashed lines show the results for ypolarization. Two lines almost overlap each other owing to little polarization dependence. See Media 1.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19121
(a)
(b) Fig. 5. Wavelength dependence of the LP11 mode rotator when (a) LP11a mode or (b) LP11b mode is input.
3. Characteristics Figure 5 shows the calculated wavelength dependence of the LP11 mode rotator when (a) LP11a mode or (b) LP11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 5, the wavelength dependence of the conversion efficiency is negligible (more than 90% over a wavelength range from 1.45 μm to 1.65 μm), and the crosstalk to the input LP11 mode is less than −20 dB over a wavelength range from 1.5 μm to 1.6 μm for both polarizations. Figure 6 shows the fabrication tolerance of the LP11 mode rotator when LP11a mode is launched at a wavelength of 1550 nm. The conversion efficiency is insensitive to fabrication errors and the crosstalk to the input LP11 mode is less than −20 dB when t, d, and s change by ± 0.3 μm, ± 0.4 μm, and ± 0.1 μm, respectively. The actual fluctuation through PLC fabrication will depend on a fabrication process and it is usually in the order of submicron.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19122
(a)
(b)
(c) Fig. 6. Fabrication tolerance to (a) trench position t, (b) trench depth d, (c) trench width s when LP11a mode is input at a wavelength of 1550 nm.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19123
(a)
(b)
(c) Fig. 7. Wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of the design parameters shown in Table 1 (t = 2.0 μm, d = 5.4 μm, and L = 1.46 mm) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19124
(a)
(b)
(c) Fig. 8. Wavelength dependence of the normalized output power for the case of t = 1.0 μm, d = 4.3 μm, and L = 1.92 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19125
(a)
(b)
(c) Fig. 9. Wavelength dependence of the normalized output power for the case of t = 0 μm, d = 3.9 μm, and L = 2.99 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19126
Next, we consider reducing the crosstalk to undesired modes such as LP01 mode and the input LP11 mode. Figure 7 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched into the mode rotator with the design parameters shown in Table 1. From Fig. 7(a), LP01 mode is output (without polarization conversion) when LP01 mode is input. This is because the optical axis for the LP01 mode is not rotated by the small trench. As shown in Fig. 7, the crosstalk to the undesired modes is less than −16 dB over a wavelength range from 1.45 μm to 1.65 μm. The crosstalk can be improved by making the parameters related to the trench smaller values. Figure 8 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of t = 1.0 μm, d = 4.3 μm, and L = 1.92 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched. From Figs. 7 and 8, we can see that the crosstalk to the undesired modes is reduced from −16 dB to −18 dB when the trench parameters are set to be smaller values. Figure 9 shows the calculated wavelength dependence of the normalized output power of LP01, LP11a, and LP11b modes for the case of t = 0 μm, d = 3.9 μm, and L = 2.99 mm (the other parameters are not changed) when (a) LP01 mode, (b) LP11a mode, or (c) LP11b mode is launched. The crosstalk to the undesired modes is reduced from −16 dB to −23 dB when the trench parameters are set to be smaller values as shown in Figs. 7 and 9.
Fig. 10. Fabricated LP11 mode rotator with silica-based PLC. All components are fabricated on a chip. Upper and lower waveguides do not have and have the trench, respectively.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19127
Fig. 11. Experimental setup for the LP11 mode rotator. PLC-based mode multiplexers are used for excitation of LP11a mode.
4. Fabrication Figure 10 shows the fabricated LP11 mode rotator using silica-based PLC with the target structural parameters shown in Table 1. All components shown in Fig. 10 are fabricated on a chip. Figure 11 shows the experimental setup for the LP11 mode rotator. In the experiment, we observed near field patterns of output light through a waveguide with or without the trench when LP11a mode is input. LP11a mode should be output when LP11a mode is input to the waveguide without the trench. On the other hand, rotated LP11 mode (ideally LP11b mode) should be output when LP11a mode is input to the waveguide with the trench. We used the PLC-based two-mode multiplexer [8] to excite LP11a mode. Table 2 shows the near field patterns of output light through the waveguide with (the left column of Table 2) or without (the right column of Table 2) the trench when LP11a mode is input at each wavelength. The reason of rotation of LP11 mode with the change of wavelength is because the optimum half beat-length for 90 degree rotation is depending on the wavelength. From Table 2, we can confirm that the fabricated LP11 mode rotator converts LP11a mode to LP11b mode over a wide wavelength range from 1460 nm to 1600 nm. We can obtain PLC-based three-mode (de)multiplexer for LP01, LP11a, and LP11b modes when we utilize the proposed LP11 mode rotator and the two-mode (de)multiplexer [8]. Figure 12 illustrates the schematic drawing of the PLC-based three-mode multiplexer that can multiplex and demultiplex LP01, LP11a, and LP11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers [8] and the proposed LP11 mode rotator. Two-mode multiplexers are used for excitation of LP11a mode. All components can be fabricated on a chip. LP11b, LP01, and LP11a modes are output when LP01 modes are launched to port 1, port 2, and port3, respectively.
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19128
Table 2. Near Field Patterns of Output Light Through the Fabricated Waveguide with (Left) or without (Right) a Trench when LP11a Mode is Input at Each Wavelength Index profile
With a trench
Without a trench
Wavelength
1460 nm
1480 nm
1500 nm
1520 nm
1540 nm
1550 nm
1560 nm
1580 nm
1600 nm
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19129
Fig. 12. Schematic drawing of PLC-based three-mode multiplexer that can multiplex and demultiplex LP01, LP11a, LP11b modes. The three-mode multiplexer consists of two PLC-based two-mode multiplexers and the proposed LP11 mode rotator. Two-mode multiplexers are used for excitation of LP11a mode.
5. Conclusion We have designed and fabricated the PLC-based LP11 mode rotator for the excitation of LP11b mode. Numerical simulations showed that converting LP11a mode to LP11b mode could be achieved with high conversion efficiency (more than 90%) over a wide wavelength range from 1450 nm to 1650 nm. Numerical simulations also showed that the LP11 mode rotator could convert LP11b mode to LP11a mode, had little polarization dependence, and had a good fabrication tolerance. It was clarified that the crosstalk to the undesired modes could be suppressed by making the trench smaller. We finally fabricated the proposed LP11 mode rotator using silica-based PLC and confirmed that the fabricated LP11 mode rotator can convert LP11a mode to LP11b mode over a wide wavelength range. We can realize the PLCbased three-mode (de)multiplexer for LP01, LP11a, and LP11b modes when we utilize the proposed LP11 mode rotator and the two-mode (de)multiplexer [8].
#212622 - $15.00 USD Received 22 May 2014; revised 25 Jun 2014; accepted 29 Jun 2014; published 30 Jul 2014 (C) 2014 OSA 11 August 2014 | Vol. 22, No. 16 | DOI:10.1364/OE.22.019117 | OPTICS EXPRESS 19130
